Question

упростите выражение!

Answer 1

$frac{a+b}{a^2+ab+b^2} * frac{a^3-b^3}{b^2-a^2} : (1 - frac{1+b}{b}) = \ \ = frac{a+b}{a^2+ab+b^2} * frac{(a-b)(a^2+ab+b^2)}{(b-a)(b+a)} : ( frac{-1}{b} ) = \ \ = frac{a-b}{b-a} * frac{-b}{1} = - frac{b-a}{b-a} * (-b) = -(-b) = b$

Answer 2

$frac{a+b}{a^2+ab+a^2} * frac{a^3-b^3}{b^2-a^2} : ( 1 - frac{1+b}{b} )= \ \ = frac{a+b}{a^2+ab+a^2} * frac{(a-b)(a^2+ab+b^2)}{-(a^2-b^2)}: ( frac{1*b - (1+b)}{b} ) = \ \ = frac{a+b}{a^2+ab +b^2} * frac{(a-b)(a^2+ab+b^2)}{-(a-b)(a+b)} : frac{b -1-b}{b} = \ \ = frac{a+b}{a^2+ab+b^2} * (- frac{a^2+ab+b^2}{a+b} ) :( -frac{1}{b} ) = \ \ = - 1 * (- frac{b}{1} ) = \ \ = - 1 * (-b) = b$